I doubt much of the public has even tried to look at Gray Davis' tax returns. The oft-mentioned counterexample here is Sen. Daschle, but there are other, less famous politicians who refuse, too. Most people just do not care about other people's tax returns beyond the curiosity of other people's incomes.
the only reason I can imagine for him thinking that he wouldn't ultimately have to reveal that information
How about privacy for himself, for his business partners, and for his family?
No. He voluntarily chose to run for Governor of California. In doing so he gave up his expectation of privacy. Else he's an idiot.